Distribution of domain sizes in the zero temperature Glauber dynamics of the one-dimensional Potts model

1996/09/01 by Bernard Derrida, Reuven Zeitak · 2 citations
Physics and Astronomy · #Opinion Dynamics and Social Influence #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics

paper · doi:10.1103/physreve.54.2513

openalex publication_date 1996/09/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

For the zero temperature Glauber dynamics of the q-state Potts model, we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one-species coagulation model (A+A\ensuremath→A). In the long time limit, this distribution is universal and, from its (complicated) exact expression, we extract its behavior in various regimes. Our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently. Considering the dynamics of domain walls as a reaction-diffusion model A+A\ensuremath→A with probability (q-2)/(q-1) and A+A\ensuremath→\ensuremathθ with probability 1/(q-1), we calculate the pair correlation function in the long time regime. \textcopyright 1996 The American Physical Society.

Citations

• Toeplitz matrices, translation kernels and a related problem in probability theory
• Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts models

Cited by

• Observable dependent quasiequilibrium in slow dynamics
• General solutions for multispin two-time correlation and response functions in the Glauber–Ising chain

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